2009 Fiscal Year Final Research Report
Study of first order model theory and its application
| Project/Area Number |
19540111
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
TSUBOI Akito University of Tsukuba, 大学院・数理物質科学研究科, 教授 (30180045)
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| Co-Investigator(Kenkyū-buntansha) |
IKEDA Kazuma 聖徳大学, 児童学部, 講師 (10383449)
SAKAI Ko 筑波大学, 大学院・数理物質科学研究科, 准教授 (20241797)
IKEDA Koichiro 法政大学, 経営学部, 教授 (60332029)
KIKYO Hirotaka 神戸大学, 工学部, 教授 (80204824)
SHIOYA Masahiro 筑波大学, 大学院・数理物質科学研究科, 准教授 (30251028)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 数学基礎論 |
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| Research Abstract |
We extended Steinhorn's omitting types theorem. His theorem holds when the theory T is superstable. We weakened the assumption of superstablity to a weaker condition of supersimlicity. Steinhorn's original proof uses the notion of average types. Our proof does not use such a notion. First we proved a quite general result and then, by applying the result to a model of supersimple theory, we get the following extension of Steinhorn's result as a corollary :
The result : Let L be a countable language and T a complete supersimple theory formulated in L. Let M be a countable model of Thaving an infinite independent (in the sense of forking) set. Suppose that M omits a complete type p over the empty set. Then there is a proper elementary extension N of M that also omits p.
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[Presentation] On coheir extentions2010
Author(s)
Akito Tsuboi
Organizer
Model Theory Kirishima 2010, New developments of "independence" in model theory
Place of Presentation
Ryokojin-sanso, Kagoshima, Japan
Year and Date
2010-03-03
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